API reference¶
exampy
¶
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exampy.
square
(x)[source]¶ The square of a number
Parameters: x (float) – Number to square Returns: Square of x Return type: float
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exampy.
cube
(x)[source]¶ The cube of a number
Calculates and returns the cube of any floating-point number; note that, as currently written, the function also works for arrays of floats, ints, arrays of ints, and more generally, any number or array of numbers.
Parameters: x (float) – Number to cube Returns: Cube of x Return type: float Raises: No exceptions are raised. See also
exampy.square()
- Square of a number
exampy.Pow()
- a number raised to an arbitrary power
Notes
Implements the standard cube function
\[f(x) = x^3\]History:
2020-03-04: First implementation - Bovy (UofT)
References
[1] A. Mathematician, “x to the p-th power: squares, cubes, and their general form,” J. Basic Math., vol. 2, pp. 2-3, 1864.
exampy.integrate
¶
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exampy.integrate.
riemann
(func, a, b, n=10)[source]¶ A simple Riemann-sum approximation to the integral of a function
Parameters: - func (callable) – Function to integrate, should be a function of one parameter
- a (float) – Lower limit of the integration range
- b (float) – Upper limit of the integration range
- n (int, optional) – Number of intervals to split [a,b] into for the Riemann sum
Returns: Integral of func(x) over [a,b]
Return type: float
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exampy.integrate.
simps
(func, a, b, n=10)[source]¶ Integrate a function using Simpson’s rule
Parameters: - func (callable) – Function to integrate, should be a function of one parameter
- a (float) – Lower limit of the integration range
- b (float) – Upper limit of the integration range
- n (int, optional) – Number of major intervals to split [a,b] into for the Simpson rule
Returns: Integral of func(x) over [a,b]
Return type: float
Notes
Applies Simpson’s rule as
\[ \begin{align}\begin{aligned}\int_a^b \mathrm{d}x f(x) \approx \frac{(b-a)}{6n}\,\left[f(a)+4f(a+h/2)+2f(a+h)+4f(a+3h/2)+\\\ldots+2f(b-h)+4f(b-h/2)+f(b)\right]\end{aligned}\end{align} \]See also
exampy.integrate.riemann()
- Integrate a function with a simple Riemann sum